Cost Benefit Analysis 笔记

本文是成本效益分析的笔记，教材是 Suzanne Bonner 的「Social Cost Benefit Analysis and Economic Evaluation」

L1 - Intro to Social CBA

Cost-Benefit Analysis (CBA) is: A process of identifying, measuring and comparing the social benefits and social costs of an investment project, program or policy intervention, from a public interest perspective.

Major Steps in a CBA

• Specify the set of options
• Decide whose benefits and costs count
• Identify the impacts and select measurement indicators
• Predict the impacts over the life of the proposed regulation
• Monetise (attach dollar values to) impacts
• Discount future costs and benefits to obtain present values
• Compute the net present value of each option
• Perform sensitivity analysis
• Reach a conclusion

Economic evaluations focus on societal perspective

A private or public sector project has implications for:

• Employment
• Government expenditure – provision of services
• The Economy
• The Environment
• Government revenue – taxes, charges

Types of Market Failure

• Externalities
• Public goods
• Incomplete information
• Uncompetitive market structures

Net Social Benefit (NSB) = Total Social Benefit - Total Social Cost

• NSB > 0 improves welfare
• Larger NSB = more efficient resource allocation
• a potential Pareto improvement

Types of CBA Analyses

• CBA is used for both prospective (appraisal) and retrospective (evaluation)
• Ex ante (or prospective) CBA
  • conducted prior to the decision to implement a new policy
  • Ex ante analysis is most useful
• Ex post (or retrospective) CBA
  • conducted at the end of the intervention and all of the
  • effects have been realized
• In medias res CBA
  • conducted during the intervention - after the decision to proceed, but before all impacts have occurred
  • is continuation of this policy a good idea?
• Comparative CBA
  • compares the ex ante analysis to an in medias res or ex post analysis of the same project (very few of these comparisons have been conducted)

Not all costs and benefits can be easily quantified in monetary terms

L2 - Discounting and Decision Rules

shadow price: when market prices are adjusted to reflect true values

The discount rate is NOT the inflation rate

• Discounting is based on the concept of time preference
• Inflation refers to changes in prices over time

Discounting Single Period

Future Value Analysis

• 𝐹𝑉 = 𝑋(1 + 𝑖)

Present Value Analysis

• PV = Y / (1 + i)
• Perpetuity PV = Y/i

Net Present Value Analysis

• all the benefits (B) minus all costs (C) of a project (including the initial investment)
• NPV = PV(B) - PV(C)

Discounting Multiple Periods

Projects Over Multiple Years

• $FV=PV(1+i)^{t}$
• $PV=\frac{FV}{(1+i)^{t}}$
• Discount Factor (or PV factor) = $\frac{1}{(1+i)^{t}}$

$NPV=\sum_{t=0}^{n}{\frac{NB}{(1+i)^{t}}}$

• where NB (Net Benefit) = B - C

Decision Rule

• NPV > 0: Undertake (Accept)
• NPV < 0: Reject

Internal Rate of Return (IRR): The discount rate at which the NPV = 0

• Can have multiple solutions for IRR

The IRR Decision Rule I

• IRR > r: Accept
• IRR < r: Reject

Hurdle Rate

• the lowest rate of return a project or investment must achieve before a manager or investor deems it acceptable
• often used in the private sector / private perspective CBA

Crossover Rate: the rate of return (or WACC) at which the NPV of two projects are equal

Benefit-Cost Ratio (BCR): BCR = PV(B) / PV(C)

• Accept if BCR >= 1

L3 - Discounting Continued

Beginning of Year Discounting: $PV=\frac{FV}{(1+i)^{t-1}}$

Mid-Year Discounting: $PV=\frac{FV}{(1+i)^{t-0.5}}$

The End of Year Discounting result is more conservative.

Comparing Non Mutually Exclusive Projects

Project	A	B	C	D	E
PV Capital Cost	400	500	300	150	100
PV Ongoing Cost	50	25	30	10	10
PV Benefits	1000	1200	200	300	125
Net Benefits (NPV)	550	675	-130	140	15
NB/PV(CapCost)	1.38	1.35	-0.43	0.93	0.15
Rank	1	2	5	3	4

Rank using ratio of net benefit to capital cost

Different budgets:

• $900 - A + B
• $1000 - A + B + E
• $500 - B (> A + E)

Comparing Projects with Different Time Frames

Equivalent annual net benefit method (EANB)

Equivalent annual net benefit (EANB) identifies a yearly annuity received for the life of a project.

• It is possible to convert any given amount or, any cash flow into an annuity

EANB = NPV / Annuity Factor (AF)

Annuity Factor: the sum of the discount factors over the life of the project where the stream of net benefits follows a fixed annuity format

$DF = \frac{1}{(1+dr)^t}$

Year	Net Benefit	DF
0	-800
1	400	0.9434
2	400	0.89
3	400	0.8396

Therefore, AF = 2.6730

Since this is a geometric series, we can also calculate with the following formula

$AF = \frac{1-(1+dr)^-t}{dr}$

NPV = $269.20

EANB = 296.20 / 2.6730 = 100.71 per year

If annuity in perpetuity: AF = 1 / dr

Pros of EANB

• it annualizes the NPV allowing for a per year net social benefit comparison between projects on a per year common metric
• results in a consistent decision when comparing projects with unequal lives

Limitation

• project comparison is the selection of the discount rate

Example EANB using Annuity Factors

Project A is a solar farm. It has NPV of $20 and a life of 25 years

Project B is a hydroelectric plant has a NPV $30 million and continues in perpetuity

The annuity factor, at 4 percent is:

• 15.62 for 25 year project
• 25 for perpetuity

EANB A = 20/15.62 = 1.28 million

EANB B =30/25 = 1.20 million

If the projects are mutually exclusive, project A should be selected as it has a higher EANB

Roll-Over Method

Project X – has a life of six years, an initial cost of $60,000 and a yearly net benefit stream of $15,000

Project Y – has a life of three years, an initial cost of $40,000 and a yearly net benefit stream of $20,000

Assuming dr = 6%

Year	Project X	Project Y
0	($60,000)	($40,000)
1	$15,000	$20,000
2	$15,000	$20,000
3	$15,000	$20,000
4	$15,000	($20,000)
5	$15,000	$20,000
6	$15,000	$20,000

Note: Project Y Year 4 = -$40000 + $20000

$NPV_{roll over}=NPV_1+\sum\frac{NPV_1}{(1+dr)^{(t-n)}}$

• $NPV_1$ = initial NPV of the project for the normal life span
• dr = discount rate
• t = total number of periods required for the roll-over
• n = initial project duration

NPV_X = $13,759.86

NPV_Y = $13,460.24 + $13,460.24/(1.06)^3 = $24,761.72

Terminal (Horizon) Values

The costs or benefits associated with a project may continue years into the
future beyond the project scope

Horizon Values

• considers cost / benefit far future seperately
  • in some cases the scrap value is used as the horizon value
• long "near future" discounting period
  • = assuming a zero horizon value

If horizon value is perpetuity: PV = FV / dr

Dealing with Inflation

nominal dollars - nominal discount rate

real dollars - real discount rate

Real interest rate: r = (i - m) / (1 + m)

• r = the real interest rate
• i = nominal interest rate
• m = inflation rate

Example: If the nominal interest rate is 5% and the inflation rate is 2% then the real interest rate is?

r = (0.05 - 0.02) / (1 + 0.02) = 2.94%

L4 - Standing and Perspectives

Four Perspectives

Market Perspective (cash flow for the overall project)

• at market prices
• irrespective of who the gainers or losers are
• ignores market failures and market distortions

Private firm / Investor Perspective

• Firms are profit maximisers
• Interested in their own profitability
• Costs are outflows of cash to a business at market prices.
• Benefits are inflows at market prices.
• Uses market perspective and accounts for loans, interest paid, depreciation and taxes.

Social Perspective

• All impacts from a policy, program, or project must be accounted for in the analysis
• Shadow prices are used to reflect the true value of goods and services

Distributional / Disaggregated Social Perceptive

• Distribution of the benefits/costs
  • disaggregating the results to the various stakeholders with standing.
• Kaldor-Hick Criterion: a policy is more efficient as long as there is a net gain to society as this enables compensation between winners and losers of a project, resulting in a net gain to society

Market Perspective (Market CBA)

The market perspective will account for tangible market transactions

• initial investment costs to implement or start a project including working capital,
• salvage / horizon values and
• ongoing benefits and costs that accrue over the life of the project
• All financial inflows and outflows
• All measured using market prices

Deriving Market Perspective

• Inflation
  • Use constant prices with a real discount rate (otherwise, nominal prices with nominal interest rate).
  • If the prices you are using do not contain inflation then you cannot use a market based discount rate.
• Incremental rather than total cash flow?
  • Consider when to use ‘with project’ less ‘without project’ cash flow.
• Depreciation excluded from market perspective cost to avoid double counting (discussed last week).
• Horizon Value, ‘Scrap Value’ or ‘Salvage’ added to cash flow in last year
• Working capital appear under investment costs at beginning and end of project
  • Only account for changes in working capital
  • Must be reversed out at the end of the project
• Interest on debt excluded from market perspective to avoid double counting
• Sunk Costs are ignored
  • already incurred
  • cannot change past decisions
  • no opportunity costs involved

Investor Perspective (Private CBA)

Deriving Investor Perspective

• The investor or private perspective refers to cash flow to the individual investor engaged in project
  • at market prices
  • after allowing for loan service costs
  • after payment of profits taxes
• Costs are outflows of cash to a business at market prices.
• Benefits are inflows at market prices.
• Uses market perspective and accounts for loans, interest paid, depreciation and taxes.
• We subtract from the Market Perspective:
  • Debt/financing inflows and outflows to creditors.
  • Taxes paid to government
• The remaining net benefit is the return to the investor from the investor’s own funds or ‘equity’
  • Market cash flow minus debt cash flow = cash flow on equity (before tax)
  • Cash flow on equity is the residual: what is left over after servicing debt
• The two items that are not part of the project’s market cash flow that enter into the calculation
• taxable profits are:
  • depreciation
  • interest on debt
  • Note: should be added to the operating costs

After Tax Cash Flow

• Profit before tax = Revenue – Operating Costs – Depreciation – Interest Paid
• Equity after tax = Net Private Benefit – Taxes Liable

Note: Ensure to subtract any loan repayments from the net private benefit (market benefit – loan repayments)

Gearing Example

Gearing: the relationship / ratio of a company's debt-to-equity (D/E) ratio

Year	0	1	2	3	4	5
Net Benefit (Market)	-5,000	1,150	1,150	1,150	1,150	1,650
Loan (Principal + Interest)	-2,500	554	554	554	554	554
Net Private Benefit (Equity)	-2,500	596	596	596	596	1,096

Notice that:

• Market Net Benefit = Debt Finance + private Equity
• IRR Market ≠ IRR Debt + IRR Equity

In this example:

• IRR Market = 7.51%
• IRR Debt = 3.50%
• IRR on Market = proportion of debt × IRR Debt + proportion of equity × IRR Equity
• 7.51% = 0.5 × 3.5% + 0.5 × IRR Equity
• IRR Equity = 5.76%

Gearing Example 2

Assume the debt-to-equity ratio is $60:$40. If the Market IRR = 10%, and cost of debt = 5%. What is the IRR on equity (approx.)?

IRR on Market CBA = 0.6(IRR on debt) + 0.4(IRR on equity)

10% = 0.6(5%) + 0.4x

IRR on equity = x = 7/0.4 = 17.5% (approx.)

L5 - Predicting and Monetising

CBA allows you to select policies which achieve allocative (Pareto) efficiency from a set of potential projects

• Allocative efficiency is where social surplus is maximised
• no one can be made better off without making someone else worse off

Kaldor-Hicks Criterion

Mutually exclusive projects – select largest NSB as it provides the largest gain to society

Potential Pareto Improvement is NSB > 0 – winners compensate losers

Kaldor-Hicks compensation: those who are made better off by a policy or project could in theory compensate those who are made worse off if NSB>0

• produces a pareto improvement
• If compensation occurs, leads to actual Pareto improvement
• Actual compensation does not actually have to occur

Limitations

• Compensation does not actually occur
• Does not consider relative wealth position
• Must be able to approximate WTP/WTA
  • Willingness to Pay / Willingness to Accept

Evaluating Direct Market Impacts

In a perfectly competitive market, the allocation is Pareto optimal

• MSB = MSC
• in efficient markets

Impacts on social surplus - evaluate the effects in markets
associated with a policy or project

Changes in social surplus:

• Basis for measuring costs and benefits
• Opportunity cost to value inputs that polices have diverted from other uses.
• Willingness to Pay to value outputs

Outputs = Benefits, Inputs = Costs

• depending on the policy there will be effects on the input and output markets

Shadow prices are required when there are market distortions or market failure

• Represent the true value of the good or service

$\delta SS=\delta SS_{output}+\delta SS_{input}$

• $\delta SS_{output}$ = change in social surplus in the output market
• $\delta SS_{input}$ = change in social surplus in the input market
• Benefits are measured from output markets
• Costs are measured from input markets

Measuring Benefits - WTP

Benefits are measured by willingness-to-pay (WTP) in the
output market

• WTP = D = MB
• P decrease -> CS increase

Measuring Costs - OC

costs are measured by opportunity costs

• These are the costs of implementing a policy or project
• Cost of Production = Opportunity Cost
  • Resources that could have been used to produce other goods and services
• Economic Rent = Producer Surplus
  • Producer surplus is the gain to suppliers of a good or service in the form of economic rent
• OC = S = MC

Market Equilibrium and Social Surplus

Perfectly competitive markets are also Kaldor-Hicks efficient (ΔSS = ΔCS + ΔPS)

Elasticity

Relative elasticities will influence the results of a intervention in a market

Elasticity changes as we move along a single curve

Government Surplus – Intervening in Markets

ΔSS = ΔCS + ΔPS + ΔGS

• ΔCS = change in consumer surplus
• ΔPS = change in producer surplus
• ΔGS = change in government surplus
• If the ΔSS > 0, the project should be undertaken

For output markets we consider the following:

• Government providing the good or service to the market
• Government reducing the cost of production
• Government controlling the price of a good

For input market, the government purchases the input which affects the demand

Government Affecting Supply in an Output Market (WTP)

Gov Providing the Good or Service to the Market

Perfectly Elastic Demand

• Government supplies q’
• Consumer surplus is unchanged (zero)
• Producer surplus is unchanged
• Government surplus is equal to q’ × P₁
• Market price is unchanged

General Case

• Government supplies q’
• Consumer surplus increases
• Producer surplus decreases (crowded out)
• Government surplus is equal to q’ × P₂
• Market price falls

Perfectly Inelastic Supply

• Government supplies q’
• Consumer surplus increases
• Producer surplus decreases
• Government surplus is equal to q’ × P₂
• Market price falls

Gov Reducing the Cost of Production

General Case

• Government reduces marginal cost
• Consumer surplus increases
• Producer surplus increases (due to lower MC)
• Government surplus is unchanged (no cost to government)
• Market price falls

Government Controlling the Price of a Good

Examples include:

• Price Ceilings (maximum price of bread)
• Price Floors (minimum wages)

These interventions are complex and can create market failures

Government Purchasing from Input Markets (OC)

Horizontal Supply

• Government demands q′ units
• Government expenditure increases by q′ × P₁
• No change in consumer surplus
• No change in producer surplus (zero)

Vertical Supply

• Government demands q′ units
• Price increases from P₁ to P₂
• No change in consumer surplus
• Producer surplus increases

General Case

• Government demands q′ units
• Consumers of the input lose B + D
• Producers gain B + D + G
• Government expenditure D + E + F + G + H + I
• Net social cost is D + E + F + I + H
  • This is the opportunity cost!

If the cost to the government is close to the opportunity cost, we can use the government expenditure to value the impact in the input market

If the cost is not close to the government expenditure, you can create a “Shadow Price” which is the average of the new price and the old price.

Change in Total Social Surplus

To evaluate the effects of a policy or project on the markets involve, we can look at the change in total social surplus

$\Delta SS = \underbrace{\Delta SS_{output}}_{\Delta CS+\Delta PS+\Delta GS} + \underbrace{\Delta SS_{input}}_{\Delta CS+\Delta PS+\Delta GS}$

Overall we have seen that the change in total social surplus will determine if a policy is welfare improving

L6 - Predicting and Monetising (cont.)

Predicting vs. Monetising

One of the most crucial aspects of a CBA involves the assessing, predicting and monetising of impacts for consideration in a policy, program or project

• Prediction concerns identifying the impacts that will occur in the future
• Monetising is quantifying the predictions in a common currency metric

Sources of Errors in Predicting Impacts

Three major sources of error must be confronted:

Omission errors, the exclusion of impacts with substantial costs and benefits, prevent CBAs from being comprehensive

• How large would the monetized value of excluded impact have to be to change the sign of NB?

Forecasting errors arise simply because we cannot predict the future with certainty

• Psychological biases: overly optimistic
  • e.g. Brisbane airport link
• Forecasts of infrastructure projects for resources may be too low
• Forecasts of regulatory impacts may fail to anticipate offsetting behaviours
  • e.g. Alcopop tax designed to reduce teenage binge drinking
  • e.g. War on Bikies

Valuation errors occur because we often do not have confident estimates of appropriate shadow prices for converting each predicted impact into an opportunity cost or a willingness to pay

• e.g. value of lost habitat, national pride, safety

CBA analysts should anticipate the errors inherent in their efforts and consciously assess them to the greatest extent possible

CBA must be effectively and independently ’de-biased’ before serving as a basis for decision making.

Benefit Value Transfers

Step 1 – identify whether existing studies or values can be used as part of the transfer method

Step 2 – decide whether the existing values from the study are appropriate for use in the CBA under consideration

Step 3 – evaluate the quality of the research being used as part of the transfer

Step 4 – make any appropriate adjustments to reflect the true value of the impact under consideration in the CBA

Methods to Predict Impacts

(1) Simplify by Predicting Incremental Impacts Relative to the Status Quo

• Impacts are predicted relative to the status quo.
• Analysts need not assess impacts that will be the same under an alternative policy as the status quo.
• Suppose alternative criminal justice policy uses the same real resources as the status quo policy: incremental resources would be zero. For example - Speed limits, drinking age

(2) Predict Using Data from an On-Going Policies or Projects

• Sometimes the relevant policy questions are whether a policy in place should be continued, terminated, or replicated.
• Inferences about impacts of the on-going policy can sometimes serve as the basis for predicting impacts to inform answers to the policy questions.
• When data on a policy is available, we “look back (make inferences) to look forward (make predictions).”
• The best basis for prediction usually comes from inferences drawn from an experimental design with random assignment of subjects into treatment and control groups.
  • e.g. training programs
• More often, inferences must be made in the absence of a true control group through a quasi-experimental design.
• These designs address the fundamental question about the observed impacts of a policy:
  • what would have happened in the absence of the policy?
• Sometimes the only available comparison may be statistics on the general population or findings from research done for other purposes.
  • Consider intervention program aimed at supporting patients with schizophrenia in community – no explicit control or comparison group.
  • The suicide risk or hospital utilization rates for schizophrenics may be drawn from the medical literature and compared to those observed for the policy being assessed.

(3) Predict on the Basis of a Similar Policy or a Series of Similar Policies

• Benefit transfer method.
• An evaluation of a policy similar to the one being analyzed may be available.
• Its value as a basis for prediction depends on how closely it matches the policy being considered and how well the evaluation was executed.
  • Quality of source, assumptions, time frame, setting

(3) Questions to ask:

• Does the policy have the same underlying model?
  • Usually, only comparisons of policies with the same underlying model will be appropriate.
• How closely do the details of the policies conform?
  • Even if the underlying models are the same, the details of the policy may differ in terms of types and intensity of intervention.
• What is the quality of the evaluation of the similar policy?
  • Is it based on an experiment? If not, does the quasi-experimental design provide a good basis for inference?

(3) Limitations of single study evaluations

• Even when its evaluation design is sound, basing prediction on a single study risks predictions of effects that are too extreme for several reasons.
• Because of the bias of academic journals to publish studies with statistically significant results, there may be other studies that did not find statistically significant effects. Consequently, the one published study may show an unrepresentative effect.
• People tend to bring cognitive biases to their decision making, including forecasting, that tend to lead to overoptimistic predictions. This optimism bias should be guarded against by analysts when they are predicting the consequences of policies they favor.
  • e.g. Brisbane airport link tunnel
  • Some analysts routinely discount the size of effects from studies in which the evaluator was closely associated with the design or implementation of the program.

(4) Predictions Based on Meta-Analyses of Similar Policies

• A meta-analysis is a study that uses a series of previous studies – highlighting the differences and similarities.
• Meta-analysis, seeks to use the information in the studies to find an effect size and its variation. Another Benefit transfer method.
• Drawing information from multiple evaluations reduces the chances that the overall result will suffer from the limitations of any one of the evaluations.
• When multiple evaluations are relevant to predicting impacts in the CBA it is worth considering investing resources into a meta-analysis due to the wealth of information.
• Often meta analysis is done on price elasticities before their use in a CBA.
  For example, meta-analyses are available for the price elasticity of fuel, residential water use, electricity, and cigarettes.
• A policy may effectively change the price of a good.
• Absent relevant evaluations of the policy itself, it may be possible to predict impacts using elasticities.
• A price elasticity of demand for the good could then be used to predict a change in the quantity of the good consumed.
  • Elasticities have been used a lot in environmental and social interventions such as air pollution, noise pollution, environmental conservation, drug interventions etc.
  • Helps estimate the WTP for the policy or program of interest without starting from scratch

(4) Meta-analyses have the following elements:

• Deep is identification of relevant past research
  • Social scientists often limit their reviews to published evaluations
  • Cost-benefit analysts often expand their coverage to unpublished studies to find more evaluations relevant to newer policies or to counter publication bias
  • i.e., limiting publication to studies with statistically significant results
• Standardisation of the effect size to a common metric such as dollars, percentages, standard deviations to enable comparisons
  • Application of a standardized measure of size effect to facilitated comparisons across studies.
  • e.g., a meta-analysis of educational interventions might convert the gains in different achievement tests to changes in standard deviations.

(5) Consult Experts

• Sometimes it is just not possible to find any quantitative evidence to help predict an impact.
• As a prediction must be made—excluding the impact is equivalent to predicting it is zero with certainty—one must turn to logic and theory to identify its plausible range.
• It may be able to obtain advice to help you make guesstimates from experts who have developed tacit knowledge from their experience.
• Remember there are issues of bias with this method (under or over estimating is likely)
• Experts may have rules-of-thumb that help them make reasonable predictions about impacts.
• There may be value in consulting multiple experts in a systematic way.
• The best-know approach for doing this is the Delphi Method. It requires participation by a number of experts.
  • Derive mean/median score

Monetising

• After predicting the impacts, we then need to monetize the impacts.
• Monetising is quantifying the predictions in a common currency metric.
  • This allows for direct comparison of the costs and benefits associated with a project.
  • The majority of costs and benefits encountered in a project will conform to quantification
• At this stage we apply the fundamental principles of willingness-to-pay and opportunity cost we have learned so far in the course.
• Monetising when Impacts Change Quantities Consumed in Markets
  • Estimated demand and supply schedules to facilitate application of methods
  • For distorted or missing markets, analysts must find appropriate shadow prices

Problems of Quantification

For a given project it is likely to be difficult to quantify all aspects of that project.
A number of key challenges often exist in attempting to obtain and apply values to certain
costs and benefits associated with a project.

Possible cause of quantification problems:

• absence of a working market
• market failures
• distortions due to government interventions

(1) Absence of markets for a cost or benefit

• For example, consider a road improvement project which is estimated to result in a reduction in fatalities on a section of road which averages 10 deaths per year.
• Problem:
  • how to apply a monetary value to the lives saved from the road improvement.
  • What value would you apply to a life?
  • Hint: use Benefit Value Transfers

(2) No appropriate market value exists due to market failure or distortions

• Consider the value of an acre of park land
• It has a market value, equal to the current market valuation for an acre of land in a particular geographical location.
• However, this market value does not reflect that this may be the only park within a 10 mile radius, and that the park may be a habitat to rare wildlife.
• The market value therefore represents an inappropriate valuation of the parkland.

L7 - Implementing Social CBA

Shadow Pricing Decisions

• In competitive market equilibrium there is only one price as determined by the intersection of supply and demand curves
• When markets are distorted there are two prices: one reflecting demand conditions (Pb) and one reflecting supply conditions (Ps)
• Shadow Pricing - adjusting observed market prices to reflect marginal benefit or cost to economy in CBA evaluations
• Shadow Pricing in Social CBA - The CBA analyst has to decide whether Pb or Ps is the appropriate price to value output or input in the CBA.

Types of Distorted Markets

• Monopoly
• Distortive Taxes
• Distortive Subsidies
• Information Asymmetries
• Public Goods
• Externalities
• Corrective Taxes and Subsidies
• Monopsony
• Labour Markets with Minimum Wages

General Rules

• Output markets:
  • If the intervention causes the availability of the output to increase – use WTP
  • If the intervention decreases the availability of the output for use by others to (diverting use) – use OC
• Input Markets:
  • If the intervention causes the availability of the input to increases – OC
  • If the intervention decreases availability of the input for use by others (diverting use) - WTP

Material Inputs / Outputs with Indirect Tax

In a perfectly competitive market, we would face supply curve S and demand curve D

• Equilibrium Price and Quantity would be P₁ and Q₁ respectively
• Implementing an ad valorem (proportional tax) decreases the supply to S_tax
• Per unit tax amount is P_b - P_s
• The area of A + B is the revenue for the tax
• C + D is the deadweight loss caused by the tax (hence distortionary)

Input Market:

• If the number of additional units sourced increases use Ps (the OC)
• If input diverted from use by other users, use Pb (the WTP)

Output Market:

• If output satisfying additional demand, use Pb (the WTP)
• If output replaces other suppliers use Ps (the OC)

Material Inputs / Outputs with Subsidy

The aim of a subsidy is to lower the market price

• Supply curve S represents the marginal cost of producing the good or service
• The supply to customers is S_subsidy which captures the cost of production minus the subsidy paid by the government
• The area of A + B + C + D + E + F + G + H is the expenditure by the government
• E + F is social deadweight loss (market distortion)
• Choice of P_b or P_s relies on whether it is an input or output market

Input Market:

• If the production of the market increases to meet the additional demand, use P_s (the OC)
• If the availability of the input is diverted from other users, use P_b (the WTP)

Output Market:

• If output increases such that it satisfies additional demand, use P_b (the WTP)
• If output replacing other suppliers, use P_s (the OC)

Calculating Taxes and Subsidies

Taxes and subsidies drive a wedge between the price the buyer pays, P_b, and the price the seller receives, P_s:

• For an ad valorem tax: P_b = P_s(1+t), i.e. P_b > P_s
• For a specific tax: P_b = P_s + t, i.e. P_b > P_s
• For an ad valorem subsidy: P_b = P_s(1-s), i.e. P_b = P_s - P_s.s, i.e. P_b < P_s
• For a specific subsidy: P_b = P_s - s, i.e. P_b < P_s

Monopoly Output

• If the government is purchasing the good from the monopoly output market use P_m
• If the government intervention increases the production of the monopoly output use P₁
• In between P_m and P₁ when production is increased but not by the full amount

Externalities

The shadow price that should be used is the one that captures the true value of the good or service.

• Negative Externality: In this instance it would be the point where MSC = MB (shown in graph)
• Positive Externality: In this instance it would be the point where MC = MSB

Asymmetric Information

Market prices value for outputs (or inputs) inaccurately in a cost-benefit analysis.

The type of asymmetric information will determine the shadow price used.

• Search and experience goods can be resolved at P₁
• Credence goods are complicated
• Search costs can be calculated

Labour Input with Minimum Wage

A minimum wage (eg. an award wage) creates a market distortion which results in excess supply of labour (unemployment)

The market equilibrium is determined by the quantity of labour demanded at the minimum wage. At this equilibrium quantity there are, in effect, two prices of labour:

• the price indicated by the demand curve (P_M the minimum wage)
• the price indicated by the supply curve (P_OC the reservation wage - the wage required to induce an extra unit of supply)

Due to the higher wage Pm

• only Q_d is demanded
• Q_s is supplied by workers

The difference between Q₂ and Q₃ is unemployment (involuntary)

If a firm higher workers at Pm it affects their value of marginal product of labour (VMP)

What wage do we use in the social CBA?

• Opportunity Costs! (the value of the labour in the next alternative use)
• shadow price = P_OC (If the workers are hired from the pooled of unemployed people)
• shadow price = P_M (If the labour was employed elsewhere)

If the labour is receiving unemployment benefits, the shadow price should capture

• P_OC: the opportunity cost to the economy
• The subsidy received to the worker (in the form of the benefit)

Corrective Taxes Vs Distortionary Taxes

Taxes and subsidies change economic behaviour:

• A tax (subsidy) on a commodity reduces (increases) quantity traded in the market place.
• The effect of a tax or subsidy is usually seen as distorting economic behaviour
  • i.e., moving the economy further away from the point at which MSB = MSC.
• However, some taxes are corrective (Pigovian taxes)

Taxes are designed to counter the negative effects on the efficiency of resource allocation resulting from missing or incomplete markets

• e.g., taxes on alcohol and tobacco are intended to discourage over-consumption from a social point of view.
• Other examples:
  • petrol excise
  • carbon tax
  • subsidies on flu vaccinations

When a project output increases in availability, or when a project input is diverted from current uses, the appropriate price is a point on a demand curve.

When a project output diverts the consumption of the output by others, or when a project input increases the availability, the appropriate price is a point on a supply curve.

We usually consider taxes and subsidies to be distortionary unless we have specific information to the contrary.

Corrective Tax

If the corrective tax is set at the efficient level it is equal to the marginal external cost. The following shadow price rules apply:

• In input markets a corrective tax should use P_b (e.g. petrol)
• In output markets a corrective tax should be P_s (e.g. tobacco)

Corrective Subsidy

If the corrective subsidy is set at the efficient level it is equal to the marginal external benefit. The following shadow price rules apply:

• In input markets a corrective subsidy should use P_s
• In output markets a corrective subsidy should be P_b

L8 - Disaggregated Social CBA

Why Disaggregated Social CBA?

• A Market evaluation will only capture benefits and costs which are fully measured by market prices
• It fails to capture various public interest aspects of a project
  • employment benefits
  • indirect tax revenue changes
  • pollution costs
• An social perspective does not provide the information on who the benefits accrue to

Disaggregating Benefits

How do we identify the various categories of disaggregated net benefits?

• Follow the financial flows
  • division of project profits between group members
  • identify direct and indirect tax flows
  • e.g. business income tax, sales tax, tariffs
• Learn from the shadow-prices
  • where there is a shadow-price the Market analysis has failed to pick up an social net benefit that must be assigned to various groups

L9 - Ethical and Social Issues in CBA

Social issues are distinct from economic issues

• environmental issues (e.g. degradation)
• distribution of wealth and income
• poverty and inequality
• crime and corruption
• gambling
• homelessness

Ethics vs. Morals

• Ethics: What should I do?
• Morals: How things should work

Utilitarianism

Utilitarianism (功利主义 / 效益主义): determines right from wrong by focusing on outcomes

• It is a form of onsequentialism (结果主义 / 效果论)
• Efficiency is a normative criterion derived from utilitarianism

Utilitarian assumption： the sum of the individual utilities should be maximized, and it is possible to trade utility gains and utility losses

• Kaldor-Hicks places economic welfare and total economic utility above other moral considerations

Deontological Ethics

Deontological Ethics (义务伦理学): whether that action itself is right or wrong under a series of rules, rather than based on the consequences of the action

• Duty or obligation-based choices
• The consequences of the action are irrelevant

Virtue Ethics

Virtue Ethics (美德伦理学): focuses on the development of a virtuous character.

• Virtues are characteristics, motivation, attitudes or dispositions that are considered favourable.
• What makes a good person, rather than what makes a good action/decision

Comparison of Ethical Theories

Utilitarian Ethics

• Definition: The greatest good for the greatest number of people
• Application: Making a decision based on what will benefit the majority to maximize the benefits to society
• Strengths:
  • Simple basis for formulating and testing policies
  • Flexible and result oriented
  • Objective in resolving self conflict
• Weaknesses:
  • It is not always possible to predict the outcome of a decision and the consequences may extend beyond the time frame.
  • Utility measures are hard to effectively determine
  • Harming a minority and benefiting a majority does not build fundamentally sound relationships.
  • Should morality be tied to happiness?

Deontological Ethics

• Definition: The action itself is right or wrong under a series of rules or duties. The consequences of the action do not matter.
• Application: Identifying one's duty and acting accordingly.
• Strengths:
  • Set of clear rules in the decision-making process based on moral laws or duties
  • Based on reason and not subjectivity
  • Emphasizes the importance of every individual
• Weaknesses:
  • Duties must be agreed upon. There may be disagreement about the principle involved in the decision.
  • The possibility of making a "right" choice that has bad outcomes.
  • Possibility of a conflict in duties.
  • Duties can change over time.
  • Moral laws can differ across societies
  • Underestimates the role of utility in decision-making

Virtue Ethics

• Definition: Focuses on the cultivation of virtues and the moral character of people.
• Application: Deciding based on characteristics that make a virtuous person.
• Strengths:
  • Not bound by rules
  • Personal "Should I do this" approach
  • Emphasis on moral development
• Weaknesses:
  • Misses the importance of obligations.
  • Potential for conflicts of virtues.
  • Does not provide a direction for the problem at or decision being evaluated
  • There is no general agreement regarding what good virtues are
  • Can be often considered "situational ethics"

Example: Giving money to a poor person on the streets

• Utilitarian: might NOT be moral if the money is subsequently used on drugs.
• Deontological: giving money to the poor is a charitable act and all charitable acts are moral regardless of the subsequent use of that money.
• Virtue Ethics: under the virtues of generosity, empathy, or selflessness, giving money to the poor is inherently good.

L10 - Dealing with Uncertainty and Sensitivity Analysis

Uncertainty and Risk

Risk can be subjective or objective

• In some situations degree of risk can be objectively determined
  • calculated from data
• Estimating probability of an event usually involves subjectivity
  • can introduce bias

Point Estimate: a single value which is a “best guess” or “best estimate” of the value

• Inputs into the CBA have been considered certain
• If the point estimates are not an appropriate starting point, then the CBA is redundant

When evaluating risk and uncertainty in CBA it is important to consider:

• what the degree of uncertainty is
• whether the uncertainty constitutes a significant risk
• whether the risk is acceptable

Expected Value

Expected Value (in CBA): The weighted average of the Net Social Benefits resulting from all possible contingencies

Investment in offshore drilling exploration where two contingencies are possible:

• Success: stock price increases from $30 to $40/share
• Failure: stock price falls from $30 to $20/share
• Objective Probability: Success (25%), Failure (75%)
• If the current stock price is $30 should we consider further exploration?

Answer:

• Expected Value of Success: ($40 - $30) * 0.25 = $2.50
• Expected Value of Failure: ($20 - $30) * 0.75 = -$7.50
• Overall Expected Value: $2.50 + (-$7.50) = -$5.00
• Therefore no further exploration

Two projects with Different Degrees of Risk

Choice depends on decision-maker’s attitude towards risk

• B has higher expected NPV, but is riskier than A
• Final choice depends on how much the decision-maker is risk averse or is a risk taker

Utility and Risk Aversion

Risk Neutral: indifferent between certain payoffs/outcomes E[U(100)] = U(100)

Risk Averse: prefers the certain amount which is less than the uncertain amount E[U(W1)] < U(100)

Risk Seeking: prefers the certain amount which is less than the uncertain amount E[U(W1)] > U(100)

Utility Curve

• Shape of indifference map shows how the decision-maker perceives risk
• Slope shows amount by which E(W) needs
• to increase to offset any given increase in risk
• The larger this amount is, the more risk
• averse the individual is at the given level of wealth
• The more risk averse the flatter the curve

Example

NB Project A: 50% = $2; 50% = $8

NB Project B: 75% = $4; 25% = $12

Expected NB:

• A = (0.5 x 2) + (0.5 x 8) = $5
• B = (0.75 x 4) + (0.25 x 12) = $6

Variance:

• A = (2 - 5)² x 0.5 + (8 - 5)² x 0.5 = $9
• B = (4 - 6)² x 0.75 + (12 - 6)² x 0.25 = $12

Which do you prefer, A or B?

B has higher expected NB but more variance (riskier), Standard Deviation (s) = √s²

• A = √9 = 3
• B = √12 = 3.46

Theory of Risk Aversion

In practice, treating expected vales as risk neutral is reasonable when pooling across a collection of policies or programs

Assume you have 50% chance of owning $36 or 50% chance of $100

• U = W^0.5
• E = (0.5x36) + (0.5x100) = $68
• Risky option or $68 with certainty?
• Expected U(W) = 0.5(10) + 0.5(6) = 8
• What certain W has U=8? W = U² = 8² = 64 (< 68)
• Certain $68 worth more than 50:50 chance of $36 or $100

Sensitivity Analysis

Sensitivity analysis: How different values of an independent variable affect a particular dependent variable under a given set of assumptions

Purpose: show how sensitive predicted net benefits are to changes in assumptions

Use IRR:If IRR > social discount rate, then this provides economic
justification for the project to go ahead.

Other Factors to Consider in a Sensitivity Analysis

• Values given to time
• Wage rates used
• The value of life, or risks associated with certain occupations
• The multiplier effect applied to the economic impact of an investment or scheme
• Environmental impacts
• Horizon Values / Salvage Values

Types of Sensitivity Analysis

• Partial sensitivity analysis:
  • How do net benefits change as one assumption varies (holding other assumptions constant)
  • It should be used for the most important or uncertain assumptions
• Best-worst case analysis
  • Can be used to find worst and best case scenarios (subset of assumptions)
  • 20% is not a bad rule of thumb
  • Does not tell the likelihood of this happening
• Simulation such as Monte Carlo
  • Creates a distribution of net benefits from drawing key assumptions from a probability distribution, with variance and mean drawn from information on the risk of the project

Partial Sensitivity Analysis Demonstration

		Units Sold
	$1,020.08	90	100	110
VC / Unit	1.5	$652.08	$1,236.56	$1,821.04
	2	$457.25	$1,020.08	$1,582.91
	2.5	$262.42	$803.61	$1,344.79

Threshold Analysis is closely related to sensitivity analysis

• Once the key variables for sensitivity testing have been identified, work out what value each would need to take for the NPV to be 0 (or, BCR=1)
• In Excel go to the “DATA” section and use the “Goal Seek” function under the “What If” key

L11 - Non-Market Valuation Methods

Total Economic Value

Total Economic Value (TEV) = Use Value + Non Use Value + Option Value

Note: Value and price are two different concepts

Role of Non-Market Valuation

Non-marketed goods and services are just as relevant to economic welfare as marketed goods and services.

Since changes in the quantities of non-marketed goods and services affect the level of economic welfare, they need to be valued in social and disaggregated CBA (but do not enter into Market or Private CBA).

The benefit value of things like:

• Nature
• Life
• Recreation
• Water quality
• Climate abatement
• Prevented diseases

The cost value of things like:

• Air pollution
• Noise
• Fishing

Non-Market Goods and Services

Shadow prices are particularly useful to address aspects of market failure in a cost benefit analysis

• estimate the shadow prices differently when there is no direct market
• Public goods (focus)
• Externalities
• Common goods (focus)

There are four types of goods in economics (based on excludability and
rivalrousness in consumption)

• Private goods: excludable and rival
  • food, clothing, cars
• Common goods: non-excludable and rival
  • fish stocks in international waters
• Mixed goods (Club Goods): excludable but non-rival
  • swimming pools, cable TV, toll roads
• Public goods: non-excludable and non-rival
  • include public parks and the air we breathe
  • street lighting, air, national defense

	Excludable	Non-Excludable
Rivalrous	Private Goods	Common Goods
Non-Rivalrous	Club Goods	Public Goods

Any given commodity lies between a pure private good and a pure public good

Non-Market Valuation Methods

There are many ways to approach non market valuation:

• Benefit Value Transfers
• Alternative Pricing Approaches
• Revealed Preferences Methods
• Stated Preference Methods

Benefit Value Transfers

Benefit Value Transfers

• Plug in values
• "Borrow" an approximate value (or a range of values) from other studies in similar situations
• Calculate prices such as
  • the social cost of carbon
  • climate laws
• Utilise non-market valuation methods to calculate the impact or value to be used in the analysis

Alternative Pricing Approaches

Indirect Market Methods

The indirect (analogous) market method uses data on similar goods in the private market to estimate the implicit "price" or the demand curve for publicly provided goods.

The market price of a comparable good in the private sector provides a good estimate of the value of a publicly provided good if it equalsthe average amount that users of the publicly provided good would be willing to pay (WTP).

Where the government provides a good or service at a lower than market price, the price paid by occupants would generally underestimate the benefit of this service because users would be WTP at least this amount (some might pay more)

• Public housing: rent = $200pm
• Private housing: rent = $500pm
• WTP between $200 & $500pm

We can use private-sector data to help map out the demand curve for a publicly-provided good if the goods and their markets are similar

Using expenditures alone underestimates total benefits because it ignores consumer surplus

Trade-Off Method

Use the opportunity cost as a measure of its value

• Time saved could be valued using the after-tax wage rate
• The wage rate is the marginal value of time
• The obvious analogous market for time saved is the labour market

Time Saved

• Wages ignore benefits
• Should take account of taxes
  • for people who are not working, use the after-tax wage rate (plus benefits)
• Ignores multitasking
  • People could be working while traveling or waiting
  • Time saved would be worth less than the wage rate (plus benefits)
• People value different types of time differently
• The wage rate may not be appropriate due to rigidities in the market or market failures
  • e.g., people may not be able to easily adjust the number of hours they work
• Firms may not pay employees their marginal social product

Using the wage rate is only a first approximation!

Value of Statistical Life (VSL): an estimate of the amount of money the public wants to spend to reduce the loss of one life.

Forgone earnings method VSL

• It suggests the value of a life saved equals the person’s discounted future earnings
  • e.g., used in compensation cases
• It generates higher values for young, high-income males than old, low-income females
• For retired people, the resultant value of life may be negative
  • e.g., medical intervention

Avoided Costs

Price on a non-market impact through the process of paying to avoid or mitigate the impact

• climate abatement costs
• double glazing to reduce noise pollution

Criticised for using price to proxy for economic surpluses

• underestimating the true value of the non-market good or service

Revealed Preference Methods

Hedonic Pricing Method

Hedonic Pricing: Assumes that the value of non-market goods and services is reflected in the price paid for goods and services (housing and land) or income received (wages), which are associated with the non-market goods and services of interest

• you would estimate a function with price as the dependent variable P = f (...)
• This method offers a way to overcome problems from omitted variables and self-selection bias

To estimate the value of a scenic view

• Estimates the effect of a marginally better scenic view on the value (price) of houses
• Estimates the WTP for scenic views after controlling for “tastes”
  • which are proxied by income and other socioeconomic factors

Two key advantages:

• The underlying application is conceptually intuitive and utilizes prices that can be observed on a market
• The results are based on revealed preferences which represent individual’s actual behaviours
  • overcome problems related to omitted variable bias and self-selection bias

Six problems:

• People must know and understand the implications of the attribute that is being valued
  • level of pollution
• Variables should be measured without error
  • house value
• The functional forms should be correct
• The market should have enough alternatives so that people can locate at their optimum point on the curve
• There may be multicollinearity problems
• Markets are assumed to adjust immediately to changes in the attributes of interest and to all other factors

Travel Cost Method (TCM)

Travel-Cost: These methods focus on expenses incurred in travelling to make use of a particular good or service

• Primarily measure the value of recreation
• full price paid to visit a recreational site > admission fee
  • opportunity cost of time spent traveling
  • costs of traveling
  • cost of accommodations
  • parking fees
• Total cost is used as an explanatory variable in place of the admission price
• Total cost faced by each person varies

Stated Preference Methods

Both Contingent Valuation (CV) and Discrete Choice Modelling (DCM) have issues with bias which is why revealed preferences are preferred over stated preference methods where possible

Contingent Valuation

Contingent Valuation is a method of estimating the value that a person places on a good.

• ask willingness to pay (WTP) to obtain a specified good
• ask willingness to accept (WTA) to give up a good
• rather than inferring them from observed behaviours in regular market places

Contingent Valuation (CV) surveys: asking a sample of people questions about their valuations

Discrete Choice Modelling

Discrete Choice Modelling estimates implicit prices for the attributes of a non-market outcome

• asking people to choose between options that are described by different levels of attributes and any costs they would have to pay

Epilogue

这个课讲了很多东西，但似乎又没学到什么。。。